Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / 2 / a

Carbon dioxide is linear, with two equivalent C–O bonds of formal bond order two; its Homo is predominantly oxygen nonbonding and its LUMO is C–O ${\pi }^{\ast }$ antibonding. The carbon uses two opposite $sp$ hybrids for its sigma bonds and two perpendicular p atomic orbitals for pi bonding. A localized $\mathrm{O}=\mathrm{C}=\mathrm{O}$ picture assigns each terminal oxygen an $s{p}^2$ sigma/lone-pair framework and one p orbital for its local pi bond.

In a symmetry-adapted description, each of the two perpendicular sets of oxygen and carbon p functions forms bonding, oxygen-centred nonbonding and antibonding combinations. The occupied nonbonding pair is labelled $1{\pi }_g$ and the lowest empty pi pair $2{\pi }_u^{\ast }$. The latter has appreciable amplitude at carbon, explaining its electrophilic reactivity. Hybridization of a terminal atom with only one bonded neighbour is a choice of localized basis, not an independently measurable bond angle; an alternative oxygen $sp$ plus p basis can represent the same delocalized system.

There are 16 valence electrons: four in the two sigma bonds, four in the two net pi bonds, and eight in the remaining oxygen lone-pair combinations. These local electron counts and the delocalized orbital description are alternative bookkeeping schemes, not additional electrons.

Ozone is bent, with two equivalent O–O bonds of approximate bond order $1.5$. Its useful localized orbital hybridization description is $s{p}^2$ at all three oxygens. Two hybrids at the central oxygen form sigma bonds and a third contains a lone pair; the three perpendicular p orbitals form a three-centre four-electron pi bond.

The three pi orbitals are bonding, nonbonding and antibonding, filled as ${\pi }_{\mathrm{b}}^2{\pi }_{\mathrm{nb}}^2{\pi }_{\ast }^0$. The terminal-centred nonbonding orbital is the Homo, conventionally $1a_2$; the delocalized antibonding orbital is the LUMO, $2b_1$. The two principal resonance structures, ${}^{-}\mathrm{O}-{\mathrm{O}}^{+}=\mathrm{O}$ and $\mathrm{O}={\mathrm{O}}^{+}-{\mathrm{O}}^{-}$, distribute the extra pi bond across the two links.

The 18 valence electrons comprise four sigma-bond electrons, ten in five sigma-framework lone pairs, and four in the pi system. This gives a paired ground-state model. More accurate treatments include electron correlation; the simple bond-order picture is not an exact charge-density calculation.^[ref]